Jacobi Elliptic Functions and the Complete Solution to the Bead on the Hoop Problem

Details Jacobi Elliptic Functions and the Complete Solution to the Bead on the Hoop Problem Jacobi Elliptic Functions and the Complete Solution to the Bead on the Hoop Problem

2012-01-20

arxiv.org/abs/1201.4201v1

Physics

Classical Physics

Accepted for publication in American Journal of Physics. 9 pages, 6 figures

Scientific paper

Jacobi elliptic functions are flexible functions that appear in a variety of problems in physics and engineering. We introduce and describe important features of these functions and present a physical example from classical mechanics where they appear: a bead on a spinning hoop. We determine the complete analytical solution for the motion of a bead on the driven hoop for arbitrary initial conditions and parameter values.

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